round 3.743 to the nearest hundredth

Answer:

range = 13

Step-by-step explanation:

The range is the difference between the largest value and the smallest value

largest value = 15 and smallest value = 2 , then

range = 15 - 2 = 13

The unit price of a mini action figures given the total cost as $18.96 is $4.74.

This is the price per each item of a particular good. We can get unit price by dividing the price of certain number of units of an item by the number of units to find the unit price of that item.

Unit price = Total price of items / total number of items.

Unit price of mini action figures = Total cost of items / Number of mini action figures

= $18.96 / 4

= $4.74

Therefore, the unit price of a mini action figures given the total cost as $18.96 is $4.74.

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Reptile stickers come in sheets of 6 and Marine Life stickers come in sheets of 9 .

Number of reptile sticker = 6

Number if marine sticker = 9C

Answer:David

Step-by-step explanation:

David saves 2:8 = 1;4 is 25%

Laura saves 3/20= 15%

Anna saves 19%

Answer:

a + c = 14

14(Pa+Pc) = 10a + 6c

224 = 10a + 6c

Step-by-step explanation:

Price of Children's tickets = $6

Price of Adult's tickets = $10

Shandra buys 14 tickets

Let

Number of adults going to the movie = a

Number of children going to the movie = c

Total price shandra pays = PaQa + PcQc

Where,

Pa = price of adult's tickets

Qa = Quantity of adult's tickets

Pc = Price of children's tickets

Qc = Quantity of children's tickets

Total price = 14(Pa+Pc), that is

a + c = 14

14(Pa+Pc) = 10a + 6c

14(10 + 6) = 10a + 6c

140 + 84 = 10a + 6c

224 = 10a + 6c

Answer:

x(xy + 1)

Step-by-step explanation:

The two terms have the common factor x.

x²y + x = x(xy + 1)

Answer:

Step-by-step explanation:

These angles are equal because the parallel lines are traversed by a straight line.

17x-6=15x+10 add 6 to each side

17x=15x+16. Subtract 15x from each side

2x=16. divide each side by 2

x=8

Answer:

Cone volume formula

To calculate its volume you need to multiply the base area (area of a circle: π * r²) by height and by 1/3: volume = (1/3) * π * r² * h

Step-by-step explanation:

Answer:

x=2

y=1

Step-by-step explanation:

-6x+12=0

take 12 to the other side &it becomes negated then equate

-6x=-12

the negatives cancel out each other and therefore the answer is positive

x=2

4y+5=9

take 5 over to the other side &it becomes negated

4y=9-5

4y=4

y=1

Step-by-step explanation:

-6x=0-12=-12= -6/-12 =2 So, X=2

4y=9-5=4 = 4/4= 1 So, y=1

Hence,

X+Y

= 2+1

=3 Answer

hope it helps

Answer:

vertical angles are =

Step-by-step explanation:

The period of the function f(x) in this problem is given as follows:

2 units.

The standard definition of the cosine function is given as follows:

y = Acos(B(x - C)) + D.

For which the parameters are given as follows:

The function for this problem is defined as follows:

f(x) = cos πx .

The coefficient B is given as follows:

B = π.

Hence the period is given as follows:

2π/B = 2π/π = 2 units.

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The proportion of the risk factor for disease X in the sample is 2/10 or 0.2.

To calculate the proportion of a specific characteristic (in this case, the risk factor for disease X) in a sample, you need to divide the number of individuals with that characteristic by the total number of individuals in the sample. In this scenario, 2 out of 10 individuals have the risk factor for disease X.

Step-by-step calculation:
1. Number of individuals with risk factor = 2
2. Total number of individuals in the sample = 10
3. Proportion of risk factor = Number of individuals with risk factor / Total number of individuals
4. Proportion of risk factor = 2 / 10
5. Proportion of risk factor = 0.2


The proportion of the risk factor for disease X in the sample is 0.2, which means 20% of the individuals in the sample have this risk factor.

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cot(θ) = cos(θ)/sin(θ)

So if both cot(θ) and cos(θ) are negative, that means sin(θ) must be positive.

Recall that

cot²(θ) + 1 = csc²(θ) = 1/sin²(θ)

so that

sin²(θ) = 1/(cot²(θ) + 1)

sin(θ) = 1 / √(cot²(θ) + 1)

Plug in cot(θ) = -2 and solve for sin(θ) :

sin(θ) = 1 / √((-2)² + 1)

sin(θ) = 1/√(5)

Answer:

1/8 of an hour

Step-by-step explanation:

3/4 x 1/6 = 3/24 = 1/8

Hope this helps!

The difference between these two amounts is $619.68

The monthly payment for a loan can be calculated using the formula:

monthly payment = \(\frac{(P * r * (1 + r)^n) }{((1 + r)^n - 1)}\)

where P is the principal (the amount borrowed), r is the monthly interest rate, and n is the total number of months in the loan term.

For Miles' loan,

P = $5,000,

r = 0.0775/12,

and n = 4 * 12 = 48.

Plugging these values into the formula, we get:

monthly payment = \(\frac{(5000 * 0.0775/12 * (1 + 0.0775/12)^{48})}{ ((1 + 0.0775/12)^{48} - 1) }\)

= $123.37

For Nick's loan,

P = $5,000,

r = 0.1310/12,

and n = 4 * 12 = 48.

Plugging these values into the formula, we get:

monthly payment =\(\frac{ (5000 * 0.1310/12 * (1 + 0.1310/12)^{48})}{((1 + 0.1310/12)^{48} - 1) }\)

= $143.34

To find out how much more Nick will have paid than Miles over the four-year period, we can subtract Miles' total payments from Nick's total payments.

Miles will make 48 payments of $123.37, for a total of:

$123.37 * 48 = $5,920.76

Nick will make 48 payments of $143.34, for a total of:

$143.34 * 48 = $6,540.32

The difference between these two amounts is:

\(6,540.32 - 5,920.76 = 619.56\)

Rounding this to the nearest cent, we get $619.68. Therefore, the answer is (a) $619.68.

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When the width of the rectangle is 6 inches and the length is 7 inches, the rate at which the area of the rectangle is increasing is 81 square inches per second.

In the given instance, a rectangle's length is growing at a pace of 3 inches per second while its width increases at a rate of 9 inches per second. We need to determine the rate at which the area of the rectangle is increasing when the width is 6 inches and the length is 7 inches.

Let W(t) and L(t) represent the width and length of the rectangle at time t, respectively. The area A(t) of the rectangle at time t is given by the formula A(t) = W(t) × L(t).

To find the rate at which the area of the rectangle is increasing, we need to differentiate the area formula with respect to time. Applying the product rule of differentiation, we have dA/dt = d(W(t) × L(t))/dt = W(t) × dL(t)/dt + L(t) × dW(t)/dt.

Substituting the given rates of change, we have dA/dt = 6 × 3 + 7 × 9 = 18 + 63 = 81.

Therefore, when the width of the rectangle is 6 inches and the length is 7 inches, the rate at which the area of the rectangle is increasing is 81 square inches per second.

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The complete question is:

The width of a rectangle is increasing at a rate of 9 inches per second and its length is increasing at the rate of 3 inches per second. At what rate is the area of the rectangle increasing when its width is 6 inches and its length is 7 inches? [Hint: Let W(t) and L(t) be the width and length, respectively, at time t.]

The rate that the area of the rectangle is increasing is ___ in² / s.  

Answer: Parallel

Step-by-step explanation:

if two secanys of a circle are made them they cut off congruent arcs

Answer:

20°

Step-by-step explanation:

4x + 5x = 180° ( being co-interior angles)

9x = 180°

x = 180°/ 9

x = 20°

Hope it will help :)

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

A

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

(2x-7)^2

Step-by-step explanation:

you need to find two numbers that add up to -28, but multiply to 196, so -14, then spread out your equation and sub in -14, then divide out common factors, and then you have your answer

if you have any questions, leave them in the comments, i will try to answer them, if this helped, pls give brainliest

Answer:

\(g(x)=4x^2-28x+49\)

\(=4(x^2-7x)+49\)

\(=4(x^2-7x+(7/2)^2-(7/2)^2)+49\)

\(=4(x-7/2)^2+4(-(7/2)^2)+49\)

\(=4(x-7/2)^2+4(-49/4)+49\)

\(=4(x-7/2)^2+0\)

\(4(x-7/2)^2+0\)

-------------------------------

so,

\(g(x)=4(x-7/2)^2+0\)

----------------------------

hope it helps....

have a great day!!

To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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Answer: A

Step-by-step explanation:

The exchange rate in 2010 should be $0.66/riyal. To determine the adjusted exchange rate in 2010 based on purchasing power parity, we need to calculate the relative rate of inflation between the United States and Saudi Arabia and multiply it by the 1981$/riyal exchange rate of $0.42.

The formula for calculating the relative rate of inflation is:

Relative Rate of Inflation = (Saudi Arabian Price Level / U.S. Price Level) - 1

Given that the Saudi Arabian price level in 2010 is 240 and the U.S. price level in 2010 is 100, we can calculate the relative rate of inflation as follows:

Relative Rate of Inflation = (240 / 100) - 1 = 1.4 - 1 = 0.4

Next, we multiply the relative rate of inflation by the 1981$/riyal exchange rate:

Adjusted Exchange Rate = 0.4 * $0.42 = $0.168

Finally, we add the adjusted exchange rate to the original exchange rate to obtain the exchange rate in 2010:

Exchange Rate in 2010 = $0.42 + $0.168 = $0.588

Rounding the exchange rate to 2 decimal places, we get $0.59/riyal.

Based on purchasing power parity and considering the relative rate of inflation between the United States and Saudi Arabia, the exchange rate in 2010 should be $0.66/riyal. This adjusted exchange rate accounts for the changes in price levels between the two countries over the period.

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The correct option is the first one, and the domain is the set of real numbers except for x = -6.

The inverse will be a function such that when we take the composition we get the identity, then we can write:

\(f(g(x)) = \frac{1}{g(x) - 4} - 6 = x\)

We need to solve that for g(x), we will get:

\(\frac{1}{g(x) - 4} - 6 = x\\\\\frac{1}{g(x) - 4} = x +6\\\\g(x) - 4 = \frac{1}{x + 6} \\g(x) = \frac{1}{x + 6} + 4\)

That is the inverse function, and notice that if x = -6 the denominator becomes zero, so that value is not in the domain.

Then the correct option is the first one.

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The value of the summation will be equal to 3.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that X=3/5, Y=1/3, and z=2⁴/₅.

The value of the Z+ ( X x Y ) will be calculated as,

E = Z + ( X x Y )

E = 2⁴/₅ + ( 3 / 5 ) x ( 1 / 3 )

E = 14 / 5 + 1 / 5

E = 15 / 5

E = 3

Therefore, the value of the summation will be equal to 3.

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Answer:659

Step-by-step explanation: